Question

If the followings are the lengths of the three sides of a triangle, then let us write by calculating, the cases where the triangles are right-angled triangles:
$9cm.,11cm$. and $6cm$.

Answer 1

Given: Three sides of the triangle are $9cm,11cm$ and $6cm$.
To check if the triangle is a right-angled triangle, we verify by Pythagoras theorem.
Taking the longest side to be hypotenuse and other two sides as base and perpendicular, we have,
Hypotenuse, $h=11cm$
Perpendicular, $p=6cm$
Base, $b=9cm$
According to Pythagoras theorem,
$$h^2=p^2+b^2$$$$\begin{array}{cc}& \Rightarrow {11}^2=6^2+9^2\\ & \Rightarrow 121=36+81\\ & \Rightarrow 121=117\end{array}$$